With less than a week to go before the Nov. 5 election, opponents of a constitutional amendment that would legalize an expansion in New York state of non-Indian casino gambling have begun to marshal resistance, setting up a battle over an important part of Gov. Andrew Cuomo's economic-development plan for upstate.

Two unlikely allies—Liz Krueger, the East Side Democrat known as one of the most liberal members of the state Senate, and Mike Long, chairman of the New York state Conservative Party—on Thursday presented the...